Given that u(t) = (e",5,cos 5t) and v(t) = (3,sin 41,4). Find [u(1) v()]. dt

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A:

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A: Given : The linear approximation at x=0 to sin(8x) is Ax + B   To Find : Value of A and B

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A: Given integral is ∫xn cos ax dx

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Q: dw where w = cos 8x sin 3y, x=- dt 5. and y=t". Use the Chain Rule to find 2

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Q: af dy of f(x, y) = tan (x²y³ + 2xy)? What is the

A: Given:     To determine:

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A: Let's find.

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A: A homogenous linear differential equation with variable coefficients given by,…

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Q: SO FO %A4 Find dy/dt. y cos(W10t +1 -sin(ot +11 5. sin(~10t + 11) II + 301 +101 sin(~10t + 11) II +…

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Q: If r = sin ( ƒ(t)), ƒ(0) = p/3, and ƒ'(0) = 4, then what is dr/dt at t = 0?

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A: Given,

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Q: If f(x,v) = ex In(5xy) find dy?

A: Given: fx,y=ex2ln5xy. To find: ∂2f∂y2 Solution: In partial derivative we differentiate with respect…

Q: The linear approximation at a = O to sin(7x) is A + Bx where A is: and where B is:

A:

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Q: Find the general antiderivative of the given function. f(x)= sin (7y)+ cos (3y)

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Q: (b) Calculate e cos(Tx) dx using integration by parts as many times as necessary.

A: Given: ∫excos(πx) dx The formula for integration by parts is given as…

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Q: dz az B. Find əx and ay 3. x eY+ cos xy36xz+5x²

A: partial derivative

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A:

Q: 3. If x = (sin t+cos t), y = (cos t-sin t), (1 < t < 4), evaluate ip, dt. dt dt

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Q: If u = x3 + y3 where x = a cos t, y = b sin t, then du dt

A: Solution

Q: The linear approximation at x = 0 to sin(4x) is A + Bx where A is: and where B is:

A:

Q: If we are integrating by parts and we have u = x² and dv = cos xdx, what are du and v?

A: given u=x2 and dv=cosxdx

Q: X Cos 9TTX² dx 2. 2. V= dTx²

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Q: If z = e* sin y, where x = s?t2 and y = s²t, by using Chain Rule find ôz/ðs and az/dt.

A: Let's find.

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Q: The linear approximation at x = 0 to sin(7x) is A + Bx where A is: and where B is:

A:

Q: The linear approximation at and where B is: = = 0 to sin(9x) is A + Bx where A is:

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Q: 1. Differentiate F(t)= e4t° sin sin 2t [Hint: y = e", u = 4t³ sin 2t.]

A: In this question we have to solve the differentiation of the function.

Q: Find, if y (3 z)t* + cosec (t) + Z In(2t + 3) dt2

A: First of all, let's get rid of Z by substituting Z = 43 in the equation above: y = (3 x 43)t4 +…

Q: If r = sin (ƒ(t)), ƒ(0) = pai/3, and ƒ′(0) = 4, then what is dr/dt at t = 0

A: Given:

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A:

Q: find ds/dt. s = sin t/1 - cos t

A: Given    S=sin t1-cos twe have to find dsdt

Q: Q: If In/x2 +y2 =sec(), use implicit differential to proof the following: - dy (²+y*). sec?. tan?…

A: lnx2+y2=secyx